The displacement $x$ of a particle in a straight line motion is given by $x = 1 - t - t^2$. The correct representation of the motion is $..............$.

For a body moving along a straight line, the following $v-t$ graph is obtained. According to the graph, the displacement during

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in the figure.
$(A)$ $A$ lives closer to the school.
$(B)$ $B$ lives closer to the school.
$(C)$ $A$ takes less time to reach home.
$(D)$ $A$ travels faster than $B$.
$(E)$ $B$ travels faster than $A$.
Choose the correct answer from the options given below:

The speed-time graph of a particle moving along a fixed direction is shown in the figure. What is the average speed of the particle over the intervals: $(a)$ $t = 0\; s$ to $10\; s$,and $(b)$ $t = 2\; s$ to $6\; s$?

$A$ particle moves along $X$-axis in such a way that its coordinate $x$ varies with time $t$ according to the equation $x = (2 - 5t + 6t^2) \ m$. The initial velocity of the particle is ....... $m/s$.